Regional trends in fish mean length at age: components of variance and the statistical power to detect trends

Abstract

We examined statewide time series (1940s–2002) of mean length at ages 2, 3, and 4 for seven fish species sampled from Michigan and Wisconsin inland lakes for temporal trends. We used a components of variance approach to examine how total variation in mean length at age was partitioned into lake-to-lake, coherent temporal, ephemeral temporal, trend, and residual variation. Using these estimated variance components, we simulated the effects of different variance structures on the power to detect trends in mean length at age. Of the 42 data sets examined, only four demonstrated significant regional (statewide) trends: age 4 largemouth bass (Micropterus salmoides) from Wisconsin lakes increased about 0.7 mm·year–1 in mean length at age, and ages 2, 3, and 4 walleye (Sander vitreus) from Wisconsin lakes decreased between 0.5 and 0.9 mm·year–1 in mean length at age. The structure of variation differed substantially among data sets, and these differences strongly affected the power to detect trends. Of particular note was that even modest levels of coherent temporal variation led to substantial decreases in power for detecting trends. To maximize trend detection capabilities, fisheries management agencies should consider variance structures prior to choosing indices for monitoring and realize that trend detection capabilities are species- and region-specific.